Method for analyzing irregularities in human locomotion

ABSTRACT

The invention relates to a method of analysis for human locomotion irregularities. In such method, acceleration measurements obtained during one or more motions controlled at a stabilized gait of a human being are used, through accelerometers measuring on a time base accelerations according to at least one direction, and any locomotion irregularities are analyzed from reference measurements. 
     Such measured accelerations are submitted to at least one wavelet transformation and the resulting wavelet transform is used to detect and/or analyze the irregularities.

This is a nationalization of PCT/FR01/00340 filed Feb. 5, 2001 andpublished in French.

The present invention relates to a method of analysis for humanlocomotion irregularities.

The invention concerns indeed the analysis of the human walking in themedical and paramedical practice, more particularly to study walkingdegradation and perform fall predictions so as to implement preventionmeasures, for example with elderly persons. The invention is alsoapplied to claudication measurements following traumas or medical orsurgical treatments. Another application field is sport walking orrunning.

Two complementary families of techniques have been developed to studythe motions of the human body and the mechanics thereof and have allowedto increase considerably the knowledge on the human locomotionphysiology:

-   -   kinematics methods that measure motions of body parts and        articular angles with the help of cinema or video images, and    -   dynamical methods that measure forces or accelerations acting on        body parts.

The kinematics methods are descriptive and bring numerous details on themotions of each body segment, but are difficult to implement. Thedynamical methods are more explicative, since they give information onthe mechanical actions causing the motion. They give that way moresynthetic information which is nevertheless very fine.

Various known measuring devices implemented in the dynamical methods(also called kinetics) are baropedometric soles, force platforms andaccelerometers. The baromedometric soles can provide a clinician withuseful data, but are not a force-measuring device. The force platformsfor their part give reliable and precise information, but the equipmentis cumbersome and expensive. Moreover, their sizes only allow for asingle bearing, which give truncated information and does not allow foran analysis of the walking variability.

The accelerometers consisting in sensors being sensitive toinstantaneous speed variations have not the above-mentioneddisadvantages and allow to obtain precise and reliable results. Seeparticularly the article from AUVINET Bernard, CHALEIL Denis and BARREYEric, “Analyse de la marche humaine dans la pratique hospitalière parune méthode accélérométrique”, REV. RHUM. 1999, 66 (7-9), pp. 447-457(French edition) and pp. 389-397 (English edition).

Measuring accelerations has this advantage to provide sensitive anddetailed information on the forces causing motions and can be simple toimplement. Moreover, conditioning and treating data are economical withrespect to the use of images. Further, acceleration measurements allowto find all the kinetics and kinematics characteristics of a motion.

The treatment of the results obtained to detect and analyze anylocomotion irregularities rests generally on Fourier transforms. Theabove-mentioned article from AUVINET and al. also proposes calculationsbased on the signal autocorrelation function (study of the symmetry andregularity of the strides) completed by a z Fischer transform to reachGauss distributions.

A disadvantage of the frequency analyses (as performed by fast Fouriertransforms) is that they need a minimum number of points to provideinformation sufficiently precise in frequency and energy. Moreover, theydo not authorise a time location of a particular event causing a quickfrequency change of the acceleration signal. Thus, it is not possible todetect a stumble being isolated amongst other regular steps. Thefrequency analysis is also badly adapted for time irregularities of thelocomotive cycle, which are not stationary, but have chaotic properties(being impredictable at short and long term).

As far as the calculation methods based on the autocorrelation functionsare concerned, they allow for a very good detection of periodicdynamical asymmetries, but are little successful to detectirregularities that are neither stationary nor periodic. They do notallow either to identify an isolated event as a sport running default ora stumble.

Moreover, several specific techniques have been developed to studycomplex motions in the equine locomotion also based on accelerationmeasurements. However, the motions being studied consist in jumps ofsport horses or gait transitions of dressage horses (change from trot togallop and vice versa), hence in transient motions. Such techniques donot apply to stabilised gait motions, such as human walking or running.

The present invention relates to a method of analysis for humanlocomotion irregularities based on acceleration measurements, whichallows to detect locomotive cycles being abnormal and irregular in time.

The method according to the invention does not require a priorimathematical properties of the studied signals, such as those needed forFourier transforms (stationary state, periodicity).

Moreover, the method according to the invention may allow for a quickand simple analysis for the results obtained.

An object of the invention is also an analysis method being able to givequantitative complementary information on the lack of dynamicalregularity in walking or running cycles.

To this end, the invention applies to a method of analysis for humanlocomotion irregularities, wherein acceleration measurements obtainedduring at least one motion controlled at a stabilised gait of a humanbeing are used, through at least one accelerometer measuring on a timebase at least one acceleration according to at least one direction, bydetecting and analysing any locomotion irregularities from referencemeasurements.

According to the invention, measured accelerations are submitted to atleast one wavelet transformation and the resulting wavelet transform isused to detect and/or analyse the irregularities.

By “stabilised gait”, it is meant a repetitive approximately periodicmotion (such as walking or running) in contrast with a transient motion.

Surprisingly, the wavelet transformation allows to locate abnormalitieswith the passing time for such a stabilised gait. Even an isolatedstumble may be detected amongst regular steps. Such a method is thusable to detect very short irregularities in contrast with the knownmethods based on Fourier transforms.

Preferentially, a spectrum of the wavelet transform is visualised inthree dimensions, respectively, of time, frequency and spectral energymodule of the wavelet transform to detect and analyse theirregularities.

The spectral energy module of the wavelet transform is thenadvantageously represented by coloured contours or a colour gradient.Further, a linear scale for time and a logarithmic scale for frequencyare advantageously used.

The direct visualisation of the wavelet offers a great readingsimplicity and allows to identify directly irregularities upon a graphicreading.

Preferentially, the wavelet transform is continuous, such a transformbeing advantageously a Morlet wavelet transform. Such symmetricalwavelets are well adapted for low frequency analyses, such as bodyaccelerations near the centre of gravity. They are given by thefollowing mathematical formula (function Ψ of variable x):Ψ(x)=k.exp(−x ²/2). cos(ω₀ x)wherein k is a normalisation constant and ω₀ is the pulse of the waveletbeing considered, preferentially comprised between 5 and 6 included. Anacceleration function Acc being dependant on time t is decomposed over afamily of wavelets of such a type by the formula:${C\left( {a,b} \right)} = {\sum\limits_{- \infty}^{+ \infty}{{{{Acc}(t)}.{\Psi\left( {{at} + b} \right)}}{dt}}}$wherein:

-   -   the coefficients C give mappings of the function Acc onto the        wavelets,    -   the parameter a is scale parameter (modification of the wavelet        stretching), and    -   the parameter b is a translation parameter (time translation of        the wavelets).

In a alternative embodiment, the transform being used is a discretewavelet transform, such as a Daubechie wavelet transform, preferably oforder 5. Such last wavelets have this property to be asymmetrical and tohave a zero order moment.

In a preferred embodiment, i.e. the wavelet transform having atime-dependant spectral energy, a low frequency band is defined in whichthe spectral energy for a regular locomotion is mainly concentrated andsaid irregularities are detected and/or analysed by using the spectralenergy outside such band. The frequency band is preferably comprisedbetween 1 Hz and 4 Hz.

The use of such a band makes for example possible two types of analysisthat can be complementary:

-   -   identification of zones of spectral energy concentrations        outside the band, and    -   spectral energy quantification out of such band.

Thus, advantageously, irregularities are identified and/or analysed bylocating and/or studying the spectral energy peaks outside the band.

Thus, for a pathological walking, high frequency peaks with asignificant energetic density exceeding the upper limit of the frequencyband (for example 4 Hz) may be observed, such peaks being more or lessperiodical and regular in time and frequency. Graphic irregularities inthe shape of such peaks are indicative of alterations in walkingdynamics and regularity.

Moreover, a locomotion irregularity degree is advantageously calculatedby reporting the margin spectral energy outside the band to the totalspectral energy.

Consequently, for a pathological walking, it can be considered that themargin energy above 4 Hz is higher than 6%.

In another advantageous analysis type based on the low frequency band,the located spectral energy values exceeding the band are measured, forexample in the case of very altered walking with high frequency patternsand quite various shape and energy.

The analyses with a wavelet transform are advantageously associated withother methods giving complementary information in the method of analysisfor human locomotion irregularities. Such information is combined withthe results obtained through wavelet transforms so as to specify the usemode for wavelets, interpret the results obtained by such waveletsand/or complete the results extracted from the analyses with wavelets.

Thus, in an advantageous embodiment, the analysis methods according toany one of the accelerations are at least in a number of two and todetect and/or analyse the irregularities, at least one vectogram (called“front butterfly”) is also used representing the intensity of one of themeasured accelerations depending on the intensity of another of themeasured accelerations. Chaotic drifts may be thus identified visuallywith respect to a stationary and periodic rate.

The accelerations used are preferentially a vertical acceleration and alateral acceleration of the subject.

In a preferred implementation, to detect and/or analyse theirregularities, at least one representation in a phase space is alsoused, giving the intensity of at least one of the accelerationsdepending on the intensity of the time derivative of such accelerationor depending on such acceleration time shifted with a predeterminedtime.

The movement of a stationary and periodic rate towards a chaotic ratecan be also identified visually. Advantageously, the acceleration beingstudied is a vertical acceleration.

In such preferred embodiment, at least one Lyapunov coefficient of therepresentation in the phase space, preferably the maximum Lyapunovcoefficient, is calculated advantageously. Thus, dynamical locomotionirregularities can be quantified, such a coefficient measuring thedeviating speed of the acceleration signal orbits within the phasespace.

Thus, the maximum Lyapunov coefficient, being calculated on acranio-caudal accelerometric signal measured at the level of the centreof gravity of a subject, quantifies globally a lack of dynamicalregularity in the walking cycles. It allows to detect temporal anddynamical fluctuations of co-ordination with respect to a risk of fall.Such global measurement of walking regularity has a clinical interestfor a prediction of the risk of fall with an elderly subject. Walkingcan be thus considered as pathological when the Lyapunov coefficientbeing used is higher than a critical value.

Thus, advantageously, it is considered that a co-ordination disorderoccurs if the maximum Lyapunov coefficient is higher than 0.4.

The device used for the accelerometers and the acceleration measurementsis preferentially conform to what is mentioned in the article fromAUVINET et al. supra. In particular, the analysis method admitsadvantageously the following characteristics, considered separately oraccording to all their technically possible combinations:

-   -   the accelerations are measured with the help of an        accelerometric sensor comprising two accelerometers arranged        according to perpendicular axes;    -   the accelerometers are incorporated into a semi-elastic        waistband secured to the waist of the subject so that they are        applied in the median lumbar region opposite the intervertebral        space L3-L4;    -   the accelerometers are arranged near the centre of gravity of        the subject (this latter being located when the person is        standing at rest before the second sacral vertebra);    -   the accelerations are measured according to cranio-caudal and        lateral axes of the subject called hereunder, respectively,        vertical and lateral axes;    -   the acceleration measurements are recorded with a portable        recorder;    -   the results obtained with the wavelet transform are completed by        obtaining the stride frequency, the step symmetry and        regularity, the symmetry and regularity variables being        advantageously submitted to a z Fischer transform;    -   the motions controlled at a stabilised gait consist in a free        walking at a comfort speed for the subject over a distance        comprised between 25 and 50 m, preferably equal to 40 m,        advantageously go and back.

Moreover, the following characteristics are advantageously implementedseparately or in combination:

-   -   the accelerations are thus measured according to a third        accelerometer, the three accelerometers being arranged according        to perpendicular axes corresponding respectively to the        cranio-caudal, lateral and longitudinal (antéro-posterior) axes        of the subject;    -   for the analysis of sport motions, the accelerations measured        are cranio-caudal and longitudinal (sagittal plane of the        subject) accelerations;    -   for the analysis of sport motions, measurements are performed        during effort tests on track or on conveyor belt;    -   a complementary Fourier frequency analysis is also implemented        in the analysis method by calculating:    -   the total spectral energy (it decreases for a pathological        walking),    -   the relative energy of the fundamental frequency which        corresponds to the step frequency (it decreases and is        distributed towards higher frequency harmonics for a        pathological walking) and/or    -   the spectrum slope calculated by a linear regression equation on        a semi-logarithmic representation of the squared spectral energy        depending on the frequency (such slope is all the more negative        since walking is altered in its temporal and dynamical        regularity).

Moreover, a sensor comprising the accelerometers, a recorder and anevent-marking device provided to mark events on the recordedacceleration signals and/or synchronize the acceleration recordings withother measuring devices (video or cinema camera, force platform, timingcell, EMG device, etc.) are advantageously used. Such device isadvantageously arranged between the sensor and the recorder andadvantageously integrated into a recording housing of the recorder.

The event-marking device has preferably activation inputs consisting inmanual electrical, optoelectronic (cell sensitive to a light flash)and/or electronic contacts.

It has preferably outputs consisting in:

-   -   a square wave emitter having advantageously a maximum value        (saturation) of a period comprised between 10 and 50 msec and        preferably 10 msec for a signal acquisition frequency at 100 Hz        advantageously emitted on the acceleration signal tracks so as        to mark such signal on a measuring point;    -   a plurality of red luminescent diodes (LED) being lightened to        provide a light signal visible on a single image with a video        camera, advantageously during a period comprised between 10 and        50 msec, preferably equal to 10 msec; and/or    -   a TTL output providing advantageously a squared signal of 5V        during a period comprised between 10 and 50 msec, preferably        equal to 10 msec.

The use of such an event-marking device is of a particular interest tomark change times (start and arrival in a walking or running test) onacceleration recordings. Thus, a spatial or cinematic marking(synchronized video film) of the recorded motion can be obtained so asto calculate the representative distances for a sport motion.

The invention also relates to the applications of the method:

-   -   in the medical field, in particular for the early detection of        neuromotor disorders of elderly subjects (it is then        particularly interesting to use the maximum Lyaponov        coefficient), and    -   in the sport field, in particular for detecting technical        defects for sport walkers or runners.

Thus, the method of the invention can be advantageously applied to thedetection of particularities of the athlete's stride during a raceperiod, such as the flight time, the bearing time, the symmetry of rightand left half-strides, the right and left propulsion and braking forcesand the race fluidity index.

The method according to the invention can also be applied to measure andquantify the biomechanical constraints due to a disease of thelocomotive apparatus, including as a function of the race speed.

The characteristic of the particularities of the athlete's stride duringthe race according to the method of the invention is useful particularlyto improve the efficiency and performance of the sportsman.

The characterization of the acceleration parameters according to themethod of the invention is useful particularly to assess the tolerancefor a disease in the locomotive apparatus as a function of the workingloads.

The present invention will be illustrated and better understood withparticular embodiments, with no limitation, referring to theaccompanying drawings, wherein:

FIG. 1 represents a subject provided with an acceleration sensor forimplementing the analysis method according to the invention;

FIG. 2 shows a measuring device useful to implement the analysis methodof the invention and corresponding to FIG. 1;

FIG. 3 shows an enlarged part of the measuring device of FIG. 2, with nosensor;

FIG. 4 represents a front sectional view of the sensor of the measuringdevice of FIG. 2;

FIG. 5 represents a top sectional view of the sensor of the measuringdevice of FIGS. 2 and 4;

FIG. 6 shows vertical and lateral acceleration curves in the timesynchronized with images of a subject for a regular walking stride;

FIG. 7 shows vertical and lateral acceleration curves in the timesynchronized with images of a subject for a pathologic walking stride;

FIG. 8 represents evolution curves in the time for vertical and lateralaccelerations for a regular walking of a subject;

FIG. 9 shows a three dimension spectral image of a Morlet wavelettransform obtained from the vertical acceleration of FIG. 8 according tothe analysis method of the invention;

FIG. 10 shows an enlarged spectral image of FIG. 9;

FIG. 11 represents a curve giving the evolution as a function of time ofthe vertical acceleration for a pathological walking of a fallingelderly subject;

FIG. 12 shows a three dimension spectral image of a Morlet wavelettransform obtained from the vertical acceleration of FIG. 11 accordingto the analysis method of the invention;

FIG. 13 is a vectogram so-called “front butterfly” giving the verticalacceleration as a function of the lateral acceleration corresponding tothe regular walking associated with FIGS. 8 to 10;

FIG. 14 represents a diagram of the vertical acceleration phases givingthe acceleration first derivative in the time as a function of thetemporal series of such acceleration for a regular walking correspondingto FIGS. 8 to 10;

FIG. 15 represents a diagram of the vertical acceleration phases givingthe acceleration first derivative in the time as a function of thetemporal series of such acceleration for a pathological walkingcorresponding to FIGS. 11 and 12;

FIG. 16 shows a three dimension spectral image of a Morlet wavelettransform obtained according to the method of the invention in a runningperiod for a sportsman the stride of whom is very fluidic;

FIG. 17 shows a three dimension spectral image of a Morlet wavelettransform obtained according to the method of the invention in a runningperiod for a sportsman having a strong propulsion and braking asymmetry.

On FIGS. 16 and 17, the upper graph shows the vertical, longitudinal andlateral acceleration curves in the time expressed in seconds; the mediangraph shows the spectral image of the wavelet transform of the verticalmotions in the time; the lower graph illustrates the spectral image ofthe wavelet transform of the longitudinal motions in the time expressedin seconds.

FIG. 18 shows vertical, antero-posterior and lateral acceleration curvesin the time synchronized with images of a subject for a regular runningstride.

A measuring device 10 (FIGS. 1 and 2) comprises a motion-sensitivesensor 16 connected with an ambulatory recorder 20 formed as a housing.

The sensor 16 is an accelerometric sensor comprising (FIGS. 4 and 5)accelerometers 201, 202 and 203 arranged perpendicularly so as to detectaccelerations respectively in the perpendicular directions 21, 22 and23. As an illustration, the three accelerometers 201, 202 and 203 areoriented respectively according a first cranio-caudal direction 21(hereafter vertical), according to a second latero-lateral direction 22and according to a third antero-posterior direction 23 (hereafterlongitudinal) of a subject 1. Such accelerometers 210-203 are sensitiveto continuous and dynamical components and are adapted for measuring lowfrequency motions. Their own frequency is for example 1200 Hz, themeasuring range being between ±10 g and the sensitivity being 5 mV/g at100 Hz. They form a cubic assembly 205 in which their orthogonality isprovided through squares 240. Such assembly 205 is moulded in asmall-size parallelepiped polymer coating 200. The coating 200 isinsulating, stiff, protective and waterproof. It has for example aheight h (direction 21), a width 1 (direction 22) and a depth p(direction 23) respectively of 40, 18 and 22 mm.

Each of the accelerometers 201, 202 and 203 is provided with fiveconnecting terminals comprising:

-   -   a mass terminal (terminals 210 and 220 respectively of the        accelerometers 201 and 202),    -   a negative power supply terminal connected with the mass        terminal (terminals 211 and 221 respectively of the        accelerometers 201 and 202),    -   a positive power supply terminal (terminals 212 and 222        respectively of the accelerometers 201 and 202),    -   a negative signal terminal (terminals 213 and 223 respectively        of the accelerometers 201 and 202), and    -   a positive signal terminal (terminals 214 and 224 respectively        of the accelerometers 201 and 202).

The terminals and the accelerometers 201 to 203 are supportedrespectively on ceramic bases 206 to 208.

The mass terminals and the negative power supply terminals of the threeaccelerometers 201 to 203 are interconnected.

The sensor 16 also comprises a wire 251 with twelve mass braidedconductors (metal braid avoiding interference) containing wiresoriginating from the power supply and signal terminals of the threeaccelerometers 201 to 203. Such wire 251, leading to the recorder 20, ispartly surrounded by a semi-rigid thermoretractable sheath 250 enteringthe coating 200. Such sheath 250 allows to avoid any breaking of thewire. It is moreover bounded outside the coating 200 by a frusto-conicalpart 252 integral with the coating 200 so as to avoid wire breakingrisks. The frusto-conical part 252 has a length L for example equal to25 mm.

Moreover, the wire 251 is provided with a clip 253 adapted to come inabutting relationship with the sheath 250 in case of the wire 251sliding in the sheath 250 so as to avoid to tear off the welds.

The sensor 16 is incorporated into a semi-elastic waistband 11 securedto the waist of the subject 1 so that this sensor 16 applies in themedian lumbar region opposite the intervertebral space L3-L4. Suchpositioning of the sensor 16 allows for a good stability of theaccelerometers near the centre of gravity of the subject 1, such centreof gravity being located before the second sacral vertebra for a humanbeing standing at rest.

The sensor 16 is arranged within a space 17 formed by a slack part 12 ofthe waistband 11 and by a leather reinforcement 13 applied against thewaistband 11 through wedges 14 and 15 made in a high density foamedfabric arranged on either side of the part 12 (FIGS. 2 and 3). Thewedges 14 and 15 allow to position the coating 200 of the sensor 16precisely within the vertebral groove of the subject 1.

The recorder 20 has for example an acquisition frequency of 100 Hz andan autonomy allowing for a continuous recording during 30 minutes. It isprovided with a low-pass filter with a cutout frequency of 50 Hz toavoid any folding phenomena. It receives three perpendicularsynchronized tracks. The acceleration measurements are digitized andcoded for example on 12 bits.

The recorder 20 comprises connection means with a treatment unit, forexample a PC type computer through a serial communication port with thehelp of a transfer software.

The measuring device 10 also comprises an event-marking device 25electrically arranged between the sensor 16 and the recorder 20 andintegrated into the housing of the recorder 20 (FIG. 2). Such device 25is adapted for marking events on recorded signals and/or synchronizeacceleration recordings with other measuring devices. It is providedwith a cell sensitive to a light flash and is adapted for saturating theaccelerometric signal for example during 0.01 second for an acquisitionat 100 Hz at the time where a flash is triggered.

In operation, the subject 1 is asked to walk on a straight line forexample over a distance of 30 m motion and 30 m back. Timing cells areadvantageously used, distant by 30 m from the ends of the path followedby the subject so as to be able to measure speeds and synchronizemeasurements. Such timing cells form each an infrared barrier comprisingand emitter and a receiver. They are respectively connected with flashesthat are triggered when the infrared barrier is crossed by the subject 1and are detected by the event-marking device 25.

Thus, the vertical and lateral accelerations are obtained in the timefor a subject 60 having a regular walking stride (FIG. 6) and a subject90 having a pathological walking stride (FIG. 7)

Thus, for regular walking, a curve 40 is represented giving the verticalacceleration (axis 32, g) and a curve 50 giving the lateral acceleration(axis 33, g) in the time (axis 32, sec). On these curves 40 and 50different walking steps are identified and they can be put in relationwith synchronized images (taken by a video camera) of the walkingsubject 60. Thus, on the curves 40 and 50:

-   -   zones 41 and 51 corresponding to an application of the left leg        90 a (image 61),    -   zones 42 and 52 corresponding to a bipodal bearing (image 62),    -   zones 43 and 53 corresponding to a lift of the right leg 90 b        and a flexion of the right knee (image 63),    -   zones 44 and 54 corresponding to a vertical unipodal bearing of        the left leg 90 a (image 64), and    -   zones 45 and 55 corresponding to a unipodal push of the left leg        90 a (image 65), are marked respectively.

Similarly, the curves 70 and 80 (FIG. 7) representing respectively thevertical and lateral accelerations in the time, on the curves 70 and 80:

-   -   zones 71 and 81 corresponding to an application of the right leg        90 b (image 91),    -   zones 72 and 82 corresponding to a bipodal bearing (image 92),    -   zones 73 and 83 corresponding to a lift of the left leg 90 a and        a flexion of the left knee (image 93),    -   zones 74 and 84 corresponding to a vertical unipodal bearing of        the right leg 90 b (image 94), and    -   zones 75 and 85 corresponding to a unipodal push of the right        leg 90 b (image 95),        are identified respectively.

The method of analysis for human locomotion irregularities based on suchresults will be described now more in detail. Thus, the attention isdrawn onto the curves 100 and 110 (FIG. 6) giving respectively thevertical and lateral accelerations (g, single axis 34 with a translationof −1 g for lateral acceleration) in the time (sec, axes 31 and 35respectively for vertical and lateral accelerations and reference axis36). Thus, cycles 101-105 are identified on the vertical accelerationcurve 100 and cycles 111-115 on the lateral acceleration curve (FIG. 6)being synchronized and corresponding respectively to motions of the leftand right steps.

Similarly, a curve 140 (FIG. 9) is obtained for example, giving thevertical acceleration (axis 32) in the time (axis 31) for a pathologicalwalking, such curve 140 admitting also cycles 141-145.

The vertical acceleration for regular walking and for pathologicalwalking is submitted to a continuous wavelet transform, for example ofMorlet type. Such transform is generally expressed by:${C\left( {a,b} \right)} = {\sum\limits_{- \infty}^{+ \infty}{{{{Acc}(t)}.{\Psi\left( {{at} + b} \right)}}{dt}}}$wherein:

-   -   the variable t is time,    -   Acc(t) is the vertical acceleration signal,    -   the function ψ(at+b) is the wavelet function used for example of        Morlet,    -   the parameters a and b of the wavelet function are respectively        the stretching (or scaling) parameter and the wavelet        translation parameter, and    -   the coefficients C(a, b) are the coefficients for the continuous        wavelet transform.

From the coefficients C (a, b), for a regular walking, a three dimensionspectral image 120 (FIGS. 7 and 8) is built up, correspondingrespectively to time, frequency and spectral energy. Such image 120 isrepresented in a plane time-frequency (or time-scale) with a linearscale for time (axis 3, sec) and a semi-logarithmic scale for frequency(axis 37, Hz). The wavelet energy module (g²) is represented by colouredcontours.

Similarly, a spectral image 150 of the Morlet wavelet transform of thevertical acceleration (FIG. 10) is obtained for pathological walkingcorresponding to FIG. 9.

The energy density on the enlargement 130 and the spectral image 150 isexpressed in acceleration (g²).

On the spectral images 120 and 150 is defined a low frequency bandhaving lower 121 and higher 122 limits associated with values of 1 Hzand 4 Hz. In the case of a regular walking, the spectrum energy densityis mainly concentrated within such band. A regular zone 123 comprisedwithin the frequency band and a pathological zone 124 located above thisband are more precisely defined.

It is observed in fact that, for a regular walking of the subject (FIG.7 and enlargement 130 of FIG. 8), the spectral energy is essentiallyconcentrated in the zone 123, periodical low peaks 125-128 appearing inthe pathological zone 124 and corresponding to walking cycles of thesubject 60.

In contrast, on the spectral image 150 associated with the pathologicalwalking of the subject 90,

-   -   a fall of the total spectral energy,    -   high frequency peaks 155-158 having a significant energy density        exceeding the limit 122 of 4 Hz, and    -   such peaks 155-158 having periodicity and regularity alterations        in time and frequency,        are observed.

The peaks 155-158 can be interpreted by stating that the moregraphically irregular their shape, the more altered are the walkingdynamics and regularity.

Besides this graphic information, quantitative information is calculatedas explained hereafter. In particular, on the spectral images 120 and150, the total quantity of spectral energy as well as the marginspectral energy on the frequency axis 37 corresponding to an energyhigher than the limit 122 of 4 Hz are determined. The data beingaccumulated on reference cases show that this margin energy is higherthan 6% for a pathological walking.

Thus, for the regular walking of example (FIGS. 7 and 8) a total energyof 22.97 g² and a margin energy representing 5.3% are obtained and, forthe pathological walking (FIG. 10) a total energy of 2.50 g² and amargin energy representing 15.4%.

In the case of a quite altered walking with high frequency patterns ofvery different form and energy, the punctual value of the energy moduleis measured on the spectral image.

Other analysis techniques complete preferably the so-obtainedinformation. In particular, it is interesting to go deeper into theinformation obtained by a frequency analysis and a calculation of thesymmetry and regularity through the autocorrelation function asindicated in the article from AUVINET et al. supra. That way:

-   -   a stride frequency of 1.00 stride per second,    -   a stride symmetry of 95.01% with a z Fischer transform of        183.25, and    -   a stride regularity of 186.27 (on 200) with a z Fischer        transform of 337.56 are obtained for the regular walking supra.    -   A stride frequency of 0.88 stride per second (too a slow        frequency),    -   a stride symmetry of 95.57% with a z Fischer transform of        189.35, and    -   a stride regularity of 160.93 (on 200) with a z Fischer        transform of 222.41 (abnormal regularity)        are obtained for the pathological walking of the example (FIGS.        9 and 10).

Such results are coupled with those obtained with the wavelettransforms. In particular, the peaks 125-128 or 155-158 are put inrelationship with the stride frequency, their right/left alternationwith symmetry and their similarity with the stride regularity.

Advantageously, such results obtained with wavelet transforms are alsocompleted through a vectogram (“front butterfly”) such as the one 160(FIG. 11) obtained for the regular walking of the example (FIGS. 6 to 8)giving the vertical acceleration (axis 32, g) as a function of thelateral acceleration (axis 33, g). On the front butterfly 160 cyclicpaths 161-163 are observed that have a tendency to be all the moresuperimposed in each other since the walking is regular. In pathologicalcases, such cyclic paths deviate from each other in an identifiable andanalysable manner.

The analysis is also completed by a phase diagram giving for example forthe vertical acceleration for regular walking (FIG. 12) and thepathological walking (FIG. 13) given as an example supra, theacceleration derivative (g.s⁻¹, axis 38) as a function of theacceleration (g, axis 32). Thus, diagrams 170 and 180 correspondingrespectively to regular and pathological walking and having respectivelycyclic paths 171-173 and 181-183 are obtained.

The irregular walking of a falling object for example is reflected by achaotic rate revealed qualitatively by a more pronounced divergence ofthe cyclic paths 181-183.

The divergence rate of the cyclic paths (or orbits) of the signal isquantified through at least one Lyapunov coefficient. Such a coefficientassesses the sensitivity of a system to deviate from a stationary andperiodical regimen from a particular point at a time to where the systemcharacteristics (starting conditions) are known.

The mean Lyapunov coefficient λ_(m) of N−1 Lyapunov coefficientsobtained with a sampling interval equal to 1 is conventionally given bya formula as follows:$\lambda_{m} = {\frac{\log\quad 2}{N - 1}{\sum\limits_{n = 1}^{N - 1}\left( \frac{1_{n + 1}}{1_{n}} \right)}}$wherein:

-   -   N is the number of points considered,    -   n is the current point number, and    -   l_(n) represents the distance between the indexed point n        belonging to an orbit and a neighbour closest point belonging to        a neighbour orbit in the phase space

A practical method for an algorithmic calculation of such a coefficientis for example found in the article from WOLF et al. “DeterminingLyapunov exponents from a time series”, in review Physica, 16D, 1985,pp. 285-317.

As an example, for a phase space dimension equal to 3 and a samplinginterval equal to 3 points, the maximum Lyapunov coefficient calculatedon the vertical accelerometric signal is comprised between 0 and 1, suchcoefficient being all the higher since the pathology increases. Thus,for a value higher than 0.4, walking is quite irregular. Thiscoefficient quantifies the lack of dynamical regularity of the walkingcycles and detects the temporal and dynamical fluctuations ofco-ordination, in relation with a fall risk.

The whole results obtained from such different methods focussed onto thewavelet analysis are combined to identify the locomotion irregularitiesand quantify them.

The above-mentioned examples based on the vertical and lateralaccelerations for walking are particularly adapted for identifyingclaudication or degradation of the capacities of elderly people so as toscreen early fall risks and to take prevention measures.

In other embodiments, other gaits are taken into consideration and/orother accelerations are used. Thus, for example, a sport walking isanalysed by using advantageously the vertical and antero-posterioraccelerations of the rachis (sagittal plane of the subject, directions21 and 23). Preferably, technical defects of a sport walking athlete arethus detected, including a knee flexion at the time of the applicationand/or a simultaneous broken contact with the ground of both athlete'sfeet.

In another embodiment, a sport race is analysed. FIGS. 16 and 17illustrate the three dimensional spectral image of a wavelet transformobtained respectively with a sportsman having a fluidic stride (FIG. 16)and a sportsman having an irregular stride (FIG. 17). FIG. 17 shows onthe longitudinal acceleration trace (upper curve <fre pro>) and thecorresponding wavelet spectrum (below), a high frequency peak at 0.2-0.4sec corresponding to an abrupt braking deceleration at the time of theapplication of the left foot. At the time 0.6-0.8, the application ofthe right foot does not show any abrupt braking, but a more pronouncedpropulsion that on the left. Such analyses of the stride allow tovisualize and characterize the stride asymmetries and to determineconsequently the biomechanical characteristics of an athlete's stride. Acomparison of the stride characteristics with the same athlete analysedat two given moments being distant in the time allow to identify thepresence of stride abnormalities characterized by changes in his or herbiomechanical characteristics. The stride analyses with said athleteaccording to the method of the invention also allow to quantify and thusto check the functional tolerance of a disease in the locomotiveapparatus of the sportsman.

In such embodiment of the method of the invention for the analysis of asport race, FIG. 18 shows the vertical, antero-posterior and lateralacceleration curves in the time synchronized with the images of thesubject.

On those curves

-   -   the bearing moment (300) of the left leg (G),    -   the mid-bearing moment (301) of the left leg (G),    -   the push moment (302) of the left leg (G), and    -   the end-bearing moment (303) of the left leg (G)        may be identified.

1. Method of analysis for human locomotion irregularities, whereinacceleration measurements obtained during at least one motion controlledat a stabilised gait of a human being are used, through at least oneaccelerometer measuring on a time base at least one accelerationaccording to at least one direction, by detecting and analysing anylocomotion irregularities from reference measurements, characterized inthat said measured accelerations are submitted to at least onecontinuous wavelet transformation and the resulting continuous wavelettransform is used to detect and/or analyse said irregularities, and thespectrum of said continuous wavelet transform is visualised in threedimensions, respectively, of time, frequency and spectral energy moduleof the continuous wavelet transform to detect and analyse saidirregularities.
 2. Method of analysis according to claim 1,characterized in that the spectral energy module of the wavelettransform is represented by coloured contours or a colour gradient. 3.Method of analysis according to claim 2, characterized in that a linearscale for time and a logarithmic scale for frequency are used.
 4. Methodof analysis according to claim 1, characterized in that said transformis a Morlet wavelet transform.
 5. Method of analysis according to claim1, characterized in that the wavelet transform having a time-dependentspectral energy, a low frequency band is defined in which the spectralenergy for a regular locomotion is mainly concentrated and saidirregularities are detected and/or analysed by using the spectral energyoutside such band.
 6. Method of analysis according to claim 5,characterized in that the band is comprised between 1 Hz and 4 Hz. 7.Method of analysis according to claim 5, characterized in thatirregularities are identified and/or analysed by locating and/orstudying the spectral energy peaks (124-128, 155-158) exceeding saidband.
 8. Method of analysis according to claim 5, characterized in thata locomotion irregularity degree is calculated by reporting the marginspectral energy outside said band to the total spectral energy. 9.Method of analysis according to claim 1, characterized in that saidaccelerations are at least in a number of two and in that, to detectand/or analyse the irregularities, at least one front butterfly (160) isalso used representing the intensity of one of the measuredaccelerations depending on the intensity of another of the measuredaccelerations.
 10. Method of analysis according to claim 1,characterized in that, to detect and/or analyse the irregularities, atleast one representation (170, 180) in a phase space is also used,giving the intensity of at least one of said accelerations depending onthe intensity of the time derivative of said acceleration or dependingon said acceleration time shifted with a predetermined time (d). 11.Method of analysis according to claim 10, characterized in that at leastone Lyapunov coefficient of said representation in the phase space,preferably the maximum Lyapunov coefficient, is calculated.
 12. Methodof analysis according to claim 11, characterized in that it isconsidered that a co-ordination disorder occurs if the maximum Lyapunovcoefficient is higher than 0.4.
 13. Application of the method ofanalysis according to claim 1 for the medical field, in particular forthe early detection of neuro-motor disorders of elderly people. 14.Application of the method of analysis according to claim 1 for the sportfield, in particular for detecting technical defects with sport walkersor runners.
 15. Application of the method of analysis according to claim1 for detecting athlete's stride particularities during a race period.16. Application of the method of analysis according to claim 1 formeasuring and quantifying the biomechanical constraints associated to adisease of the locomotive apparatus.
 17. Method of analysis for humanlocomotion irregularities, wherein acceleration measurements obtainedduring at least one motion controlled at a stabilised gait of a humanbeing are used, through at least one accelerometer measuring on a timebase at least one acceleration according to at least one direction, bydetecting and analysing any locomotion irregularities from referencemeasurements, wherein said measured accelerations are submitted to atleast one wavelet transformation and the resulting wavelet transform isused to detect and/or analyse said irregularities, and the spectrum ofsaid wavelet transform is visualised in three dimensions, respectively,of time, frequency and spectral energy module of the wavelet transformto detect and analyse said irregularities, characterized in that thewavelet transform having a time-dependent spectral energy, a lowfrequency band is defined in which the spectral energy for a regularlocomotion is mainly concentrated and said irregularities are detectedand/or analysed by using the spectral energy outside such band. 18.Method of analysis for human locomotion irregularities, whereinacceleration measurements obtained during at least one motion controlledat a stabilised gait of a human being are used, through at least oneaccelerometer measuring on a time base at least one accelerationaccording to at least one direction, by detecting and analysing anylocomotion irregularities from reference measurements, wherein saidmeasured accelerations are submitted to at least one wavelettransformation and the resulting wavelet transform is used to detectand/or analyse said irregularities, and the spectrum of said wavelettransform is visualised in three dimensions, respectively, of time,frequency and spectral energy module of the wavelet transform to detectand analyse said irregularities, characterized in that, to detect and/oranalyse the irregularities, at least one representation (170, 180) in aphase space is also used, giving the intensity of at least one of saidaccelerations depending on the intensity of the time derivative of saidacceleration or depending on said acceleration time shifted with apredetermined time (d).